How to Create a Fair and Equitable Partnership From Day One
You should certainly register your business with your state's labor department.. As for the type of entity you elect, that will depend on a variety of factors that I cannot address without knowing more information from you. For instance, a sole proprietorship would not be an option if both you and your partner intend on owning equity in the business. From what you describe, the more suitable option would likely be a partnership or S Corporation. This decision will impact how profits are distributed and accounted for in the company books.
In terms of allocating profits, it is still possible for two partners to have equal ownership in the business even if one contributes capital and the other does not. Specifically, the other partner can gain equity by contributing labor (i.e. sweat equity) and/or property.
Your first step is to have a candid conversation with your partner. Be clear on each others’ expectations and what you both see as fair. Your next step is to get these expectations in writing. Browse sample partnership agreements online to get a sense for issues you might not have considered (such as, what happens if one of you chooses to leave the business or start a competing entity). Then consider consulting with a lawyer who can help you draft something that works for your business. Many law schools offer free and low cost clinics for small business owners like yourself and there might even be one available on your campus. Experts there can help advise you and shape an agreement that works for your business.
Related: When Choosing Your Startup Partner, Opposites Really Do Attract